Research on superheavy nuclei is one of the hot points in nuclear physics [1-4].The structure and decay of heavy and superheavy nuclei are systematically studied by different models [5-12].Self-consistent mean-field models show that there is shape coexistence in the ground state of superheavy nuclei.New models of $alpha$-decay half-lives and new formulae for nuclear binding energies and spontaneous fission half-lives are presented [5-11].The theoretical results are in good agreement with available data of heavy and superheavy nuclei.The properties of unknown superheavy nuclei are predicted.